Using our new Post-Newtonian SPH ( smoothed particle hydrodynamics ) code , we study the final coalescence and merging of neutron star ( NS ) binaries . We vary the stiffness of the equation of state ( EOS ) as well as the initial binary mass ratio and stellar spins . Results are compared to those of Newtonian calculations , with and without the inclusion of the gravitational radiation reaction . We find a much steeper decrease in the gravity wave peak strain and luminosity with decreasing mass ratio than would be predicted by simple point-mass formulae . For NS with softer EOS ( which we model as simple \Gamma = 2 polytropes ) we find a stronger gravity wave emission , with a different morphology than for stiffer EOS ( modeled as \Gamma = 3 polytropes as in our previous work ) . We also calculate the coalescence of NS binaries with an irrotational initial condition , and find that the gravity wave signal is relatively suppressed compared to the synchronized case , but shows a very significant second peak of emission . Mass shedding is also greatly reduced , and occurs via a different mechanism than in the synchronized case . We discuss the implications of our results for gravity wave astronomy with laser interferometers such as LIGO , and for theoretical models of gamma-ray bursts ( GRBs ) based on NS mergers .